Precalculus Examples

$\frac{\ln (2^{- 4} \cdot 3^{- 1})}{\ln ({(3.5)}^{- 3})}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{\ln (\frac{1}{2^{4}} \cdot 3^{- 1})}{\ln ({3.5}^{- 3})}$

Step 1.2

Raise $2$ to the power of $4$ .

$\frac{\ln (\frac{1}{16} \cdot 3^{- 1})}{\ln ({3.5}^{- 3})}$

Step 1.3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{\ln (\frac{1}{16} \cdot \frac{1}{3})}{\ln ({3.5}^{- 3})}$

Step 1.4

Multiply $\frac{1}{16} \cdot \frac{1}{3}$ .

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Step 1.4.1

Multiply $\frac{1}{16}$ by $\frac{1}{3}$ .

$\frac{\ln (\frac{1}{16 \cdot 3})}{\ln ({3.5}^{- 3})}$

Step 1.4.2

Multiply $16$ by $3$ .

$\frac{\ln (\frac{1}{48})}{\ln ({3.5}^{- 3})}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{\ln (\frac{1}{48})}{\ln (\frac{1}{{3.5}^{3}})}$

Step 2.2

Raise $3.5$ to the power of $3$ .

$\frac{\ln (\frac{1}{48})}{\ln (\frac{1}{42.875})}$

Step 2.3

Divide $1$ by $42.875$ .

$\frac{\ln (\frac{1}{48})}{\ln (0.02332361)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (\frac{1}{48})}{\ln (0.02332361)}$

Decimal Form:

$1.03004348 \dots$